A182289 Triangle read by rows. Let p be one of the parts of size A135010(n,k) in one of the partitions of n and S(n,k) = sum of all preceding parts to p in the mentioned partition of n. So T(n,k) = 2*S(n,k) + A135010(n,k).

1, 3, 2, 5, 5, 3, 7, 7, 7, 6, 2, 4, 9, 9, 9, 9, 9, 8, 3, 5, 11, 11, 11, 11, 11, 11, 11, 10, 6, 2, 10, 4, 9, 3, 6, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 8, 3, 12, 5, 11, 4, 7, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 14, 10, 6

Offset: 1

Author

Omar E. Pol, Aug 14 2012

Keywords

• nonn
• tabf

Comments

Consider a physical model of the partitions of n in which each part p of size A135010(n,j) is represented by a right circular cylinder with radius j and height 2. T(n,k) is also the distance (or coordinate X) from the axis Y to the center of the base of cylinder of the part p in the structure of A135010.

Examples

			Written as an irregular triangle the sequence begins:
1;
3,2;
5,5,3;
7,7,7,6,2,4;
9,9,9,9,9,8,3,5;
11,11,11,11,11,11,11,10,6,2,10,4,9,3,6;
13,13,13,13,13,13,13,13,13,13,13,12,8,3,12,5,11,4,7;
15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,14,10,6,2,14,10,4,14,9,3,14,6,13,5,10,4,8;
		

Crossrefs

Row n starts with A000041(n-1) terms equal to A005408(n-1). Row n has length A138137(n). Right border gives A000027.

Cf. A135010.